After you select and insert a Web Part into your page, you may want to
modify its properties to fit your needs. The number and type of
properties you can modify in SharePoint 2010 are based on what type of
Web Part you use. When you select the Edit Web Part command by
clicking the Web Part menu (in the far right of the Web Part title),
SharePoint opens the Web Part tool pane. In some Web Parts, SharePoint
creates a link to this tool pane as part of the placeholder text.
Following is a list of properties in the tool pane common to List View
Web Parts:

Appearance: The Appearance section allows you to title the Web Part,
fix the height and width as necessary, and determine the chrome type.
Chrome is another word for the Web Part surround; for example, title
and border options.

3) select edit page within the ribbon (should be on the left hand side)

4) once selected the page will change to edit mode and you can now add webparts to the page. Find your webpart that you want to add the chrome... there should be a drop down arrow on the right handside of the webpart. Click it.. you should see some options. the one you want is "Edit Web Part". Select that option.

5) click "Appearance" in the new tab on the right hand side of the page

6) near the bottom you should see "chrome type". click on the dropdown and change to "Title and border". Now select apply and then ok.

You should now see the changes with your webpart wrapped in a border with title :)

or hover over the webpart and an arrow should appear on the top right side of the webpart, click it and select "Edit Web Part" and follow from 5 above!

actually what is on my page layout is NOT a webpart, it is a field(like <SharePointWebControls:TextField FieldName="fa564e0f-0c70-4ab9-b863-0177e6ddd247" runat="server"></SharePointWebControls:TextField>). So there is no edit web part option.
–
ozdoganOct 10 '12 at 11:21